The currently most widely used nuclide for imaging in clinical MRI is hydrogen nucleus (proton), which is the major constituent of subjects.
MRI realizes two-dimensional or three-dimensional imaging of forms or functions of human head, abdominal part, limbs, and so forth by imaging spatial distribution of proton density or relaxation information of magnetic resonance signals.
When a human body is an object of the measurement, as the major sources of protons that can be detected by MRI, there are water and fats. Fats existing in human bodies reduce contrast of images of the abdominal part, spine, limbs, etc. of a subject.
Therefore, there have been proposed methods for suppressing fat signals in clinical measurements. As one of them, there is known the Dixon method (Non-patent document 1), in which fat signals are suppressed by using phase difference between water and fat signals.
Hereafter, the Dixon method will be explained.
Difference of “chemical shift”, which indicates resonant frequency, between water and fats is 3.5 ppm, due to the difference in the molecular structures. The difference of the resonant frequency between water and fats is proportional to magnetic field strength, and when the magnetic field strength is 1.5 teslas, it corresponds to about 224 Hz.
The Dixon method utilizes the phase difference produced by the difference in the frequency of water and fats signals.
Data are obtained for a plurality of images with different times from excitation of nuclear spins to acquisition of signals (henceforth referred to as echo time). Specifically, images are obtained with such an echo time that water and fat signals become in-phase, and such an echo time that water and fat signals become out-of-phase.
When the frequency difference of water and fat signals is represented by df, such a time tin that the water and fat signals become in-phase is represented as n/df, and such a time tout that the water and fat signals become out-of-phase is represented as (n+½)/df, wherein n is an integer.
In the Dixon method, two of images, an image I1 and an image I2, are obtained with the echo times tin and tout, respectively.
If a water signal is represented by W, and a fat signal is represented by F, I1 and I2 can be represented by the following equations (1) and (2), respectively.I1=W+F  (1)I2=W−F  (2)
By addition and subtraction of these equations for two images, the water signal and the fat signal are separated as represented by the following equations (3) and (4).W=(I1+I2)/2  (3)F=(I1−I2)/2  (4)
On the basis of the above, each of the water signal W and the fat signal F can be calculated, and separate images of water and fats can be obtained.
However, in the Dixon method, the phase rotation induced by inhomogeneity of the static magnetic field produced when a subject is inserted into the static magnetic field space is not taken into consideration. If spatial inhomogeneity of the static magnetic field exists, phase rotation is induced depending on the position, which is different from the chemical shift, and therefore there arises a problem that water and fats cannot be completely separated by the simple addition and subtraction as shown by the equations (3) and (4).
Therefore, as water/fat separation methods that take inhomogeneity of the static magnetic field into consideration, the methods described in Non-patent documents 2 and 3 are known.
Non-patent document 2 describes a method in which a least square estimation processing is repeatedly performed with three images obtained with different echo times to determine three variables, water signal W, fat signal F, and frequency difference f induced by inhomogeneity of the static magnetic field, to separate water and fats images.
In the method of Non-patent document 3, two of images, images I1 and I2, are obtained with such an echo time that water and fat signals become in-phase, and such an echo time that water and fat signals become out-of-phase, respectively, as in the Dixon method. However, in the method of Non-patent document 3, phase rotation induced by inhomogeneity of the static magnetic field is estimated by using the region growing method, and thereby water and fats signals are separated. In addition, in the method of Non-patent document 3, after the image I1 is obtained with such an echo time tin that water and fat signals become in-phase, the gradient magnetic field pulse is reversed, and the image I2 is obtained with such an echo time tout that water and fat signals become in-phase. That is, the in-phase image and out-of-phase image are obtained by one measurement.